On the spectrum of the pencil generated by the Dirichlet problem for an elliptic equation in an angle

Leningrad. Translated fromSibirskii Matematicheskii Zhurnal, Vol. 32, No. 2, pp. 74–87, March–April, 1991.     

Change in the properties of the membrane of the left ventricle of an artificial heart after operating in an animal

Conclusion After 53-day operation of a biomer membrane of an AH in a calf its physical and mechanical properties changed little. The membrane retained the greater part of its fatigue life and a high surface quality; as a consequence of insignificant creep, its functional properties also changed little.Translated from Mekhanika Kompozitnykh Materialov, No. 3, pp. 533–536, May–June, 1985.     

Optimal investment and reinsurance of an insurer with model uncertainty

We introduce a novel approach to optimal investment–reinsurance problems of an insurance company facing model uncertainty via a game theoretic approach. The insurance company invests in a capital market index whose dynamics follow a geometric Brownian motion. The risk process of the company is governed by either a compound Poisson process or its diffusion approximation. The company can also transfer a certain proportion of the insurance risk to a reinsurance company by purchasing reinsurance. The optimal investment–reinsurance problems with model uncertainty are formulated as two-player, zero-sum, stochastic differential games between the insurance company and the market. We provide verification theorems for the Hamilton–Jacobi–Bellman–Isaacs (HJBI) solutions to the optimal investment–reinsurance problems and derive closed-form solutions to the problems.     

On M. G. Krein's papers in the theory of spaces with an indefinite metric

This is a survey of the papers by M. G. Krein (and his disciples) devoted to the theory of operators in spaces with an indefinite metric and its applications.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, Nos. 1–2, pp. 5–17, January–February, 1994.     

Consistency of the least squares estimator of an infinite-dimensional parameter

Kiev. Translated fromSibirskiî Matematicheskiî Zhurnal, Vol. 33, No. 4, pp. 65–69, July–August, 1992.     

Approximation of the ruin probability with an exponential exactness

Novosibirsk. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 32, No. 4, pp. 61–65, July–August, 1991.     

Determining an atmic Boolean algebra from the action of the automorphism group

Rudnyî. Translated fromSibirskiî Matematicheskiî Zhurnal, Vol. 34, No. 6, pp. 49–51, November–December, 1993.     

First boundary-value problem of weighted type for an elliptic equation degenerate at an interior point of the domain

Institute of Mathematics and Informatics, Lithuanian Academy of Sciences. Translated from Litovskii Matematicheskii Sbornik (Lietuvos Matematikos Rinkinys), Vol. 31, No. 3, pp. 513–522, July–September, 1991.     

Index of the center of an irreducible nilpotent linear group

Unimprovable estimates of the index of the center of an irreducible nilpotent linear group over an arbitrary field are obtained.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, Nos. 7 and 8, pp. 950–956, July–August, 1991.     

Numerical and empirical approach in predicting the penetration of a concrete target by an ogive-nosed projectile

This paper demonstrates the application of both numerical simulation and empirical equation in predicting the penetration of a concrete target by an ogive-nosed projectile. The results from the experiment performed by Gran and Frew [In-target radial stress measurements from penetration experiments into concrete by ogive-nose steel projectiles, Int. J. Impact Eng. 19 (8) (1997) 715–726] are used as a benchmark for comparison. In the numerical simulations a 3.0-caliber radius-head steel ogival-nose projectile with a mass of 2.3 kg is fired against cylindrical concrete target with a striking velocity of 315 m/s. The simulation, performed using AUTODYN 2-D, assesses three numerical schemes, namely Langrange, Euler–Lagrange coupling and smooth particles hydrodynamics SPH–Lagrange coupling, in predicting the maximum depth of penetration and the radial stress–time response of the concrete target. When assessing the three solution techniques we hypothesize that the effect of strain rate on strength for the concrete target does not adversely affect the prediction on the maximum depth of penetration and the radial stress–time response of the concrete target. In the empirical approach the penetration equation developed by Forrestal et al. [An empirical equation for penetration depth of ogive-nose projectiles into concrete targets, Int. J. Impact Eng. 15 (4) (1994) 395–405] is used to determine the maximum depth of penetration and the deceleration–time response. The deceleration–time response for the projectile using the empirical approach is compared with those obtained from the numerical simulations. Results from both the numerical and empirical approaches are consistent. The calculated depth of penetration from both approaches yield relatively good agreement with that obtained from the experiment. The numerical simulations using each of the three numerical schemes are also able to reproduce the profiles from the radial stress measurements. Simulations using the SPH numerical scheme give the best overall agreement. The good overall agreement with the experimental radial stress measurements and consistent results between both empirical and numerical approach, enhanced the confidence in engineers and ballisticians when using these two approaches in complementing full-scale testing.     

Calculation of the nonlinear viscoelastic oscillations of an antivibration layer

It is proposed to use a viscoelastic layer to protect equipment against vibration. The principal quadratic theory of hereditary viscoelasticity is used as the physical relation between the forces and displacements. The solutions obtained for the integrodifferential vibration equation make it possible to minimize the displacements and accelerations of the protected equipment.Moscow Institute of Electronic-Machine Building. Translated from Mekhanika Polimerov, No. 2, pp. 321–326, March–April, 1972.     

Effect of transverse shear on the stability of an orthotropic cylindrical shell with an elastic core in axial compression

The effect of transverse shear on the stability of a composite shell in axial compression has been investigated. The core is treated as an isotropic elastic cylinder bonded to the inner surface of the shell. The effect of the tangential shearing forces between the shell and the core is taken into account.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 2, pp. 267–273, March–April, 1973.     

On an action of the group ring of a group of field automorphisms

Novosibirsk. Translated fromSibirskiî Matematicheskiî Zhurnal, Vol. 33, No. 6, pp. 162–168, November–December, 1992.     

Solvability of an inverse problem for the parabolic equation with convergence

Novosibirsk. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 33, No. 3, pp. 42–49, May–June, 1992.     

Effect of an electron beam on the structure of epoxy resins

It is shown that exposing a cured epoxy resin to the action of an electron beam leads to a change in the structure outside the zone of direct action of the beam; this is accompanied by the formation of diffraction rings in the electron diffraction pattern and a change in microhardness.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 3, pp. 523–525, May–June, 1976.     

Experimental method of solving an integral equation of the theory of viscoelasticity

A solution of an integral equation of the theory of viscoelasticity is proposed. This solution, based on a creep test on a polymer specimen with an included elastic element, improves the convergence of the method of approximations.Moscow M. V. Lomonosov State University. Translated from Mekhanika Polimerov, No. 4, pp. 584–587, July–August, 1969.     

Parametric oscillations of an orthotropic cylindrical shell with an elastic filler I. Formulation of the problem

A linear model of a Timoshenko-type shell with an elastic filler is proposed for solving the problem of the parametric oscillations of the system. A class of operators is derived, which act in a Hilbert space, for which the problem of the determination of a spectrum of eigen-values permits an iterative scheme of solution. Thus, the method for solving problems of parametric oscillations of structures proposed by Bolotin is confirmed.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 3, pp. 470–478, May–June, 1974.     

Analytic investigation of the stress-strain relation for an arbitrary loading trajectory

The determination of the strain trajectory from a known arbitrary loading trajectory is described within the framework of the theory of slip. Specific calculations have been made on an electronic computer.Institute of Physics and Mathematics, Academy of Sciences of the Kirgiz SSR, Frunze. Translated from Mekhanika Polimerov, No. 6, pp. 981–986, November–December, 1971.     

Improvement of an inequality of Hardy containing an estimate of the size of an intermediate derivative of a function

Translated from Matematicheskie Zametki, Vol. 50, No. 4, pp. 114–122, October, 1991.